EN|RU
English version: Journal of Applied and Industrial Mathematics, 2019, 13:2, 317-326 |
![]() |
Volume 26, No 2, 2019, P. 129-144 UDC 519.1
Keywords: set, group, coset, characteristic function, progression. DOI: 10.33048/daio.2019.26.610 Alexandr A. Sapozhenko 1 Received February 20, 2018 References[1] A. A. Sapozhenko, On the number of sum-free sets in Abelian groups, Vestn. Mosk. Univ., Ser. 1, 4, 14–17, 2002 [Russian].[2] A. A. Sapozhenko, The Cameron–Erdös conjecture, Dokl. Akad. Nauk, 393, No. 6, 749–752, 2003 [Russian]. [3] A. A. Sapozhenko, Solution of the Cameron–Erdös problem for groups of prime order, Zh. Vychisl. Mat. Mat. Fiz., 49, No. 8, 1503–1509, 2009 [Russian]. Translated in Comput. Math. Math. Phys., 49, No. 6, 1435–1441, 2009. [4] V. G. Sargsyan, Asymptotics of the logarithm of the number of $(k, l)$-sumfree sets in an Abelian group, Diskretn. Mat., 26, No. 1, 91–99, 2014 [Russian]. Translated in Discrete Math. Appl., 25, No. 2, 93–99, 2014. [5] N. Alon, Independent sets in regular graphs and sum-free subsets of Abelian groups, Isr. J. Math., 73, 247–256, 1991. [6] Yu. Bilu, Sum-free sets and related sets, Combinatorica, 18, No. 4, 449–459, 1998. [7] N. J Calkin, On the number of sum-free set, Bull. Lond. Math. Soc., 22, 140–144, 1990. [8] N. J. Calkin and A. C. Taylor, Counting sets of integers, no $k$ of which sum to another, J. Number Theory, 57, 323–327, 1996. [9] N. J. Calkin and J. M. Thomson, Counting generalized sum-free sets, J. Number Theory, 68, 151–160, 1998. [10] P. J Cameron and P. Erdös, On the number of sets of integers with various properties, in Number Theory (Proc. 1st Conf. Can. Number Theory Assoc., Banff, Canada, Apr. 17–27, 1988), pp. 61–79, Berlin: de Gruyter, 1990. [11] B. Green, The Cameron–Erdös conjecture, Bull. Lond. Math. Soc., 36, No. 6, 769–778, 2004. [12] B. Green, A Szemerédi-type regularity lemma in Abelian groups, Geom. Funct. Anal., 15, No. 2, 340–376, 2005. [13] B. Green and I. Z. Ruzsa, Sum-free sets in Abelian groups, Isr. J. Math., 147, 157–188, 2005. [14] V. F. Lev, Sharp estimates for the number of sum-free sets, J. Reine Angew. Math., 555, 1–25, 2003. [15] V. F. Lev, T. Luczak, and T. Schoen, Sum-free sets in Abelian groups, Isr. J. Math., 125, 347–367, 2001. [16] V. F. Lev and T. Schoen, Cameron–Erdös modulo a prime, Finite Fields Appl., 8, No. 1, 108–119, 2002. [17] T. Schoen, A note on the number of $(k, l)$-sum-free sets, Electron. J. Comb., 17, No. 1, 1–8, 2000. |
|
![]() |
|
© Sobolev Institute of Mathematics, 2015 | |
![]() |
|